The present invention relates to a numerical optimizing method for the determination of the optical data of an objective, and it further relates to an objective that is made in accordance with the method.
Numerical optimizing methods of this kind have long been known. The textbook “Synthese optischer Systeme” (Synthesis of Optical Systems) by H. Haferkorn and W. Richter (1984; VEB Deutscher Verlag der Wissenschaften: DDR-1080 Berlin) discusses the correction of optical systems in chapter 4. The first step is to find an optimizing function which takes a multitude of image aberrations into account such as, e.g., Seidel's aberrations, transverse aberrations, or wave aberrations. The individual image aberrations can be entered into the optimizing function with individual weight factors. In addition, boundary constraints such as focal lengths, or design constraints, can also be taken into account. The optimizing function depends on the degrees of freedom of the optical system, such as for example lens radii, asphericity parameters, lens thicknesses, distances between lenses, or indices of refraction. The purpose of the numerical optimizing method is to minimize the optimizing function and to thereby determine the optical data of the optical system. A variety of methods are used for the automatic correction, such as for example the correction methods with a linear approximation of the optimizing function, or the correction methods with a quadratic approximation of the optimizing function.
The aforementioned textbook is mentioned only as an example. The fundamentals of numerical optimizing methods are also described in the English-language literature related to the field of optical design.
A widely used computer program to run numerical optimizing processes is available under the trade name “Code V®” by Optical Research Associates (ORA®), Pasadena, Calif. (USA). With the Code V® program, an optimizing function can be defined which takes a variety of image aberrations into account. With a start-up system as a point of departure, the optical data of an objective can subsequently be determined with local and global optimizing procedures.
The computer program ZEMAX® of Focus Software, Inc., Tucson, Ariz., likewise provides the capability to determine the optical data of an objective through a numerical optimizing process.
It became known in May 2001, based on measurements that had been made, that calcium fluoride, in spite of having a cubic crystal structure, exhibits the characteristics of intrinsic birefringence. The measurement results supporting this discovery have been published in November 2001 in the article “Intrinsic birefringence in calcium fluoride and barium fluoride” by J. Burnett et al. (Physical Review B, Volume 64 (2001), pages 241102-1 to 241102-4).
To discuss the subject of intrinsic birefringence, it is essential to use an unambiguous notation of the crystallographic directions. Therefore, a system of notations is introduced below to identify crystallographic directions, crystallographic planes, and lenses whose lens axes are oriented in certain crystallographic directions.
The indices for the crystallographic directions will hereinafter be bracketed between the symbols “<” and “>”, and the indices for the crystallographic planes will be bracketed between the symbols “{” and “}”. The crystallographic directions are perpendicular to the correspondingly indexed crystallographic planes. For example, the crystallographic direction <100> is perpendicular to the crystallographic plane {100}. Crystals with a cubic lattice structure, which includes the fluoride crystals that are of interest in the present context, have the principal crystallographic directions <110>, < 110>, <1 10>, < 1 10>, <101>, <10 1>, < 101>, < 10 1>, <011>, <0 11>, <01 1>, <0 1 1>, <111>, < 1 1 1>, < 1 11>, < 11 1>, <1 1 1>, < 111>, <1 11>, <11 1>, <100>, <010>, <001>, < 100>, <0 10>, and <00 1>.
Because of the symmetries of cubic crystals, the principal crystallographic directions <100>, <010>, <001>, < 100>, <0 10>, and <00 1> are equivalent to each other. Therefore, those crystallographic directions that are oriented along one of the principal directions <100>, <010>, <001>, < 100>, <0 10>, and <00 1> will hereinafter be identified by the prefix “(100)-”, and crystallographic planes that are perpendicular to these directions will also be identified by the same prefix “(100)-”. Lenses whose lens axes are parallel to one of these principal crystallographic directions are likewise given the prefix “(100)-”.
Furthermore, the principal directions <110>, < 110>, <1 10>, < 1 10>, <101>, <10 1>, < 101>, < 10 1>, <011>, <0 11>, <01 1>, and <0 1 1> are likewise equivalent to each other. Therefore, those crystallographic directions that are oriented along one of the latter group of principal directions will hereinafter be identified by the prefix “(110)-”, and crystallographic planes that are perpendicular to these directions will also be identified by the same prefix “(110)-”. Lenses whose lens axes are parallel to one of these principal crystallographic directions are likewise given the prefix “(110)-”.
Finally, the principal directions <111>, < 1 1 1>, < 1 11>, < 11 1>, <1 1 1>, < 11 1>, <1 11>, and <11 1> are also equivalent to each other. Therefore, those crystallographic directions that are oriented along one of the latter group of principal directions will hereinafter be identified by the prefix “(111)-”, and crystallographic planes that are perpendicular to these directions will also be identified by the same prefix “(111)-”. Lenses whose lens axes are parallel to one of these principal crystallographic directions are likewise given the prefix “(111)-”.
Any statements made hereinafter in regard to one of the aforementioned principal crystallographic directions should be understood to be equally applicable to the equivalent principal crystallographic directions.
Consistent with the above, the crystallographic (111)-directions are not equivalent to the crystallographic (100)-directions or the crystallographic (110)-directions. Likewise, the crystallographic (100)-directions are not equivalent to the crystallographic (110)-directions.
According to the article in Physical Review B which was mentioned above, the intrinsic birefringence is strongly dependent on the material orientation of the fluoride crystal lens and on the direction of the light ray. It reaches its maximum in a light ray traveling through a lens in the crystallographic <110>-direction. The measurements presented in the article show that rays propagating in the (110)-direction of a calcium fluoride crystal are subject to a birefringence of (−11.8±0.4) nm/cm at a wavelength of λ=156.1 nm, of (−3.6±0.2) nm/cm at a wavelength of λ=193.09 nm, and of (−0.55±0.07) nm/cm at a wavelength of λ=253.65 nm. On the other hand, if the light propagation is oriented in the <100> direction or in the <111> direction of the crystal, no intrinsic birefringence occurs in calcium fluoride, as is also predicted by theory. Thus, the intrinsic birefringence has a strong directional dependence and increases significantly for shorter wavelengths.
The directional dependence of the intrinsic birefringence in a fluoride crystal with a cubic crystal structure is shown in the published article. “The trouble with calcium fluoride” by J. Burnett et al. (spie's oemagazine, March 2002, pp. 23-25 and FIG. 4). The intrinsic birefringence of a light ray depends in this case on the aperture angle as well as on the azimuth angle of a light ray. As is made evident in FIG. 4, the intrinsic birefringence has a fourfold azimuthal symmetry if the lens axis is oriented in the crystallographic (100)-direction, a threefold azimuthal symmetry if the lens axis is oriented in the crystallographic (111)-direction, and a twofold azimuthal symmetry if the lens axis is oriented in the crystallographic (110)-direction. By rotating two fluoride crystal lenses relative to each other about their lens axes, it is possible to reduce the detrimental influence of the intrinsic birefringence. An angle of rotation of 45° is proposed for two lenses whose lens axes are oriented in the crystallographic (100)-direction, an angle of rotation of 60° for two lenses whose lens axes are oriented in the crystallographic (111)-direction, and an angle of rotation of 90° for two lenses whose lens axes are oriented in the crystallographic (110)-direction. By simultaneously using pairs of (100)-lenses, (111)-lenses, and (110)-lenses with these respective angles of rotation, it is possible to reduce the optical path difference between two mutually orthogonal states of polarization. Furthermore, using calcium fluoride lenses and barium fluoride lenses in combination likewise results in a compensation of the detrimental influence of the intrinsic birefringence because, according to FIG. 2 of the same article, the respective birefringence effects for comparable crystallographic directions in barium fluoride and calcium fluoride have opposite signs.
As described in the articles by John Burnett et al., the detrimental influence of intrinsic birefringence manifests itself most of all in objectives that are used in the deep ultraviolet range (λ<200 nm), such as for example lithography projection objectives for applications in 157 nm-lithography.
Projection objectives and microlithography projections systems of this type have been disclosed, e.g., in the Patent Application Publication WO 01/50171 A1 (U.S. Ser. No. 10/177,580), which has the same assignee as the present application, and the references cited therein. The examples of embodiments presented in that patent application are purely refractive as well as catadioptric projection objectives with numerical aperture values of 0.8 and 0.9 at working wavelengths of 193 nm as well as 157 nm. The material used for the lenses is calcium fluoride.
The not pre-published patent application PCT/EP 02/05050, which has the same assignee as the present application, gives a description of different compensation methods to reduce the detrimental influence of the intrinsic birefringence, e.g., in the objectives that are presented as examples in WO 01/50171 A1 (U.S. Ser. No. 10/177,580). Among others, the solutions disclosed therein include the parallel use of (100)-lenses with (111)-lenses or (110)-lenses of the same fluoride crystal material as well as the use of compensation coatings. The disclosure of WO 01/50171 A1 (U.S. Ser. No. 10/177,580) is hereby incorporated in its entirety in the present application.
The not pre-published patent application DE 101 33 841.4 (U.S. Ser. No. 10/199,503), which has the same assignee as the present application, proposes the concept of using lenses of two different crystalline materials in parallel in order to reduce the harmful influence of intrinsic birefringence. Calcium fluoride and barium fluoride are suggested as a suitable pair of materials. The disclosure of DE 101 33 841.4 (U.S. Ser. No. 10/199,503) is hereby incorporated in its entirety in the present application.
The concept of rotating the orientation of lens elements in order to compensate for the effects of birefringence is also described in the not pre-published patent application DE 101 23 725.1, (PCT/EP 02/04900), whose content is hereby incorporated by reference in the present application.
However, the proposed methods are limited in their capability, or work only for a small number of suitable lenses, to provide a complete compensation of the aberrations caused by intrinsic birefringence. While it is known in theory, that two (100)-lenses rotated by 45° or two (111)-lenses rotated by 60°, relative to each other will reduce the harmful effects of intrinsic birefringence, this prediction is met in the ideal sense only if the lenses are adjoining planar-parallel plates. Transferring this concept to objectives with a multitude of individual lenses with different lens thickness and different surface parameters of the lens surfaces presents itself as a serious problem to the optical designer. For one, as the number of fluoride crystal lenses gets larger, the lens materials, the orientations of the lens axes and the angles of rotation have to be determined for a larger number of lenses. As a further problem, it is normally necessary to go through a comprehensive calculation of the polarization along specific light rays in order to determine the result of the compensation. However, calculating the polarization optics along the entire paths of representative rays is a complex undertaking.